Ho did the thief manage to open the safe ?

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A thief enters a shop and threatens the clerk, forcing him to open the safe. The clerk says, "The code for the safe is different every day, and if you hurt me you'll never get the code". But the thief manages to guess the code on his own.

Thirty friends were on a hiking trip when they decided to enjoy the bonfire. They assembled for it and agreed to play a game. For that, they divided themselves in five teams with seven members each, forming five rows.

There are 13 caves arranged in a circle. There is a thief hiding in one of the caves. Each day the the thief can move to any one of of the caves that is adjacent to the cave in which he was staying the previous day. And each day, you are allowed to enter any two caves of your choice.

What is the minimum number of days to guarantee in which you can catch the thief?

Note: Thief may or may not move to adjacent cave. You can check any two caves, not necessarily be adjacent. If thief and you exchange your caves, you will surely cross at some point, and you can catch the thief immediately.

A woman depended on a public telephone to make her calls, but it was usually out of order. Each day she reported this to the phone company, but nothing was done. Finally she came up with a fib that she told the phone company. The phone was fixed the next day.

One man was pacing here and there on the road in worry when a bright woman noticed him. On asking he told her that while replacing his tire, he incidentally dropped all the four nuts into a deep drain. She told him what to do and he was then able to drive back successfully till his office.